A standard approach to optimization under uncertainty is based on original Markovitz portfolio theory and more recently was tailored to oilfield applications with modified definition of efficient frontier (U.S. Pat. No. 6,775,578 B. Couet, R. Burridge, D. Wilkinson, Optimization of Oil Well Production with Deference to Reservoir and Financial Uncertainty, 2004) and Value of Information (Raghuraman, B., Couët, B., Savundararaj, P., Bailey, W. J. and Wilkinson, D.: “Valuation of Technology and Information for Reservoir Risk Management,” paper SPE 86568, SPE Reservoir Engineering, 6, No. 5, October 2003, pp. 307-316). However, these methods employ mean-variance approach and do not provide a much needed insight into the inherent uncertainty of the optimized model and, more importantly, any quantitative guidance on reducing this uncertainty, which is very desirable from the operational point of view.
Application of Global Sensitivity Analysis to address various problems arising in oilfield industry has been described for reservoir performance evaluation, for measurement screening under uncertainty, for pressure transient test design and interpretation, for design and analysis of miscible fluid sampling clean-up, and for targeted survey design. However, these disclosures were focusing only on quantifying uncertainty in specific physical quantities and using that analysis to gain a new insight about the measurement program design and interpretation. The references did not look at optimization of the underlying physical processes.